Find the Exact Value sin((3pi)/4)cos((7pi)/4)

$\sin (\frac{3 π}{4}) \cos (\frac{7 π}{4})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (\frac{π}{4}) \cos (\frac{7 π}{4})$

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \cos (\frac{7 π}{4})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{\sqrt{2}}{2} \cos (\frac{π}{4})$

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2}$

Multiply $\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2}$ .

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2} \sqrt{2}}{2 \cdot 2}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{\sqrt{2}}^{1} \sqrt{2}}{2 \cdot 2}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}{2 \cdot 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sqrt{2}}^{1 + 1}}{2 \cdot 2}$

Add $1$ and $1$ .

$\frac{{\sqrt{2}}^{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{{\sqrt{2}}^{2}}{4}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{{(2^{\frac{1}{2}})}^{2}}{4}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2^{\frac{1}{2} \cdot 2}}{4}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2^{\frac{2}{2}}}{4}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2^{\frac{2}{2}}}{4}$

Rewrite the expression.

$\frac{2^{1}}{4}$

Evaluate the exponent.

$\frac{2}{4}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

Find the Exact Value sin((3pi)/4)cos((7pi)/4)

Related Questions

Support LCMGCF.com by disabling your adblocker.